This was a strange one that was initially fixed by simply disabling the Chrome app (v 73.0.3683.75) on my device. However, considering that the company I work for has in excess of 10,000 users across 4 continents, asking every user who had updated their phones to Android Pie to disable core functionality such as their default browser was obviously a completely impractical solution.
Digging in to the Chromium bugzilla, it appeared that there was an issue with the settings of the webview. I found that the issue could be fixed easily by setting the CacheMode property on the settings of the WebView object:
private WebView _webView;
var settings = _webView.Settings;
settings.CacheMode = CacheModes.NoCache;
Easy as that.